Abstract:Bounds on the ultimate precision attainable in the estimation of a parameter in Gaussian quantum metrology are obtained when the average number of bosonic probes is fixed. We identify the optimal input probe state among generic (mixed in general) Gaussian states with a fixed average number of probe photons for the estimation of a parameter contained in a generic multimode interferometric optical circuit, namely, a passive linear circuit preserving the total number of photons. The optimal Gaussian input state i… Show more
“…We then prove that the required non-Gaussian measurement is the POVMs constructed over the eigenbasis of the product quadrature operatorsXP +PX. The results of this work not only cover all partial results that have been discussed so far in the literature [21][22][23][24][25][26] (as shall be explained in detail throughout this work), but also offer rich conclusive discussions, with the full generality, regarding phase estimation using single-mode Gaussian states. We thus expect our general study to be fundamentally interesting, and also practically useful in cases where metrological resources are limited.…”
Section: Introductionmentioning
confidence: 78%
“…(32) being reduced to cos χ (II) DSVS = tanh(2r) is equal to F SVS of Eq. (26). Now let us turn to the case that thermal photons exist in the Gaussian probe state.…”
Section: A Optimal Gaussian Measurementsmentioning
The central issue in quantum parameter estimation is to find out the optimal measurement setup that leads to the ultimate lower bound of an estimation error. We address here a question of whether a Gaussian measurement scheme can achieve the ultimate bound for phase estimation in single-mode Gaussian metrology that exploits single-mode Gaussian probe states in a Gaussian environment. We identify three types of optimal Gaussian measurement setups yielding the maximal Fisher information depending on displacement, squeezing, and thermalization of the probe state. We show that the homodyne measurement attains the ultimate bound for both displaced thermal probe states and squeezed vacuum probe states, whereas for the other single-mode Gaussian probe states, the optimized Gaussian measurement cannot be the optimal setup, although they are sometimes nearly optimal. We then demonstrate that the measurement on the basis of the product quadrature operatorŝ XP +PX, i.e., a non-Gaussian measurement, is required to be fully optimal.
“…We then prove that the required non-Gaussian measurement is the POVMs constructed over the eigenbasis of the product quadrature operatorsXP +PX. The results of this work not only cover all partial results that have been discussed so far in the literature [21][22][23][24][25][26] (as shall be explained in detail throughout this work), but also offer rich conclusive discussions, with the full generality, regarding phase estimation using single-mode Gaussian states. We thus expect our general study to be fundamentally interesting, and also practically useful in cases where metrological resources are limited.…”
Section: Introductionmentioning
confidence: 78%
“…(32) being reduced to cos χ (II) DSVS = tanh(2r) is equal to F SVS of Eq. (26). Now let us turn to the case that thermal photons exist in the Gaussian probe state.…”
Section: A Optimal Gaussian Measurementsmentioning
The central issue in quantum parameter estimation is to find out the optimal measurement setup that leads to the ultimate lower bound of an estimation error. We address here a question of whether a Gaussian measurement scheme can achieve the ultimate bound for phase estimation in single-mode Gaussian metrology that exploits single-mode Gaussian probe states in a Gaussian environment. We identify three types of optimal Gaussian measurement setups yielding the maximal Fisher information depending on displacement, squeezing, and thermalization of the probe state. We show that the homodyne measurement attains the ultimate bound for both displaced thermal probe states and squeezed vacuum probe states, whereas for the other single-mode Gaussian probe states, the optimized Gaussian measurement cannot be the optimal setup, although they are sometimes nearly optimal. We then demonstrate that the measurement on the basis of the product quadrature operatorŝ XP +PX, i.e., a non-Gaussian measurement, is required to be fully optimal.
“…We further show in Supplementary Note 4 that, among all possible states with fixed average particle number, squeezed vacuum states optimize the sensitivity of multiparameter displacement sensing, generalizing the single-parameter results of refs. 62 , 63 . Fig.…”
Squeezing currently represents the leading strategy for quantum enhanced precision measurements of a single parameter in a variety of continuous-and discrete-variable settings and technological applications. However, many important physical problems including imaging and field sensing require the simultaneous measurement of multiple unknown parameters. The development of multiparameter quantum metrology is yet hindered by the intrinsic difficulty in finding saturable sensitivity bounds and feasible estimation strategies. Here, we derive the general operational concept of multiparameter squeezing, identifying metrologically useful states and optimal estimation strategies. When applied to spin-or continuousvariable systems, our results generalize widely-used spin-or quadrature-squeezing parameters. Multiparameter squeezing provides a practical and versatile concept that paves the way to the development of quantum-enhanced estimation of multiple phases, gradients, and fields, and for the efficient characterization of multimode quantum states in atomic and optical sensor networks.
“…1. In the regime N abs = O(1), the performance can be improved by considering more general states, such as the optimal states discussed in [66,[75][76][77][78][79][80][81].…”
We consider the estimation of a Hamiltonian parameter of a set of highly photosensitive samples, which are damaged after a few photons Nabs are absorbed, for a total time T. The samples are modelled as a two mode photonic system, where photons simultaneously acquire information on the unknown parameter and are absorbed at a fixed rate. We show that arbitrarily intense coherent states can obtain information at a rate that scales at most linearly with Nabs and T, whereas quantum states with finite intensity can overcome this bound. We characterise the quantum advantage as a function of Nabs and T, as well as its robustness to imperfections (non-ideal detectors, finite preparation and measurement rates for quantum photonic states). We discuss an implementation in cavity QED, where Fock states are both prepared and measured by coupling atomic ensembles to the cavities. We show that superradiance, arising due to a collective coupling between the cavities and the atoms, can be exploited for improving the speed and efficiency of the measurement.
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